Electrically variable vehicle transmissions (EVTs) include an input shaft connectable to an engine, an output shaft, and a plurality of planetary gearsets each having respective first, second, and third members. EVTs also include one or more electric motor/generators. Each motor/generator is operatively connected to a respective member of one of the planetary gearsets to provide a range or mode of transmission operation characterized by a continuously variable speed ratio between the input shaft and the output shaft. The continuously variable speed ratio is proportional to the speed of one of the motor/generators.